\newproblem{lay:2_7_22}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 2.7.22}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  The signal broadcast by commercial television describes each color by a vector $(Y,I,Q)$. If the screen is black and white, only the $Y$ coordinate is used (this gives a
	better monochrome picture than using CIE data for colors). The correspondence between $YIQ$ and a ``standard'' $RGB$  color is given by
	\begin{center}
		$\begin{pmatrix}Y\\I\\Q\end{pmatrix}=\begin{pmatrix} 0.299 & 0.587 & 0.114 \\ 0.596 & -0.275 & -0.321 \\ 0.212 & -0.528 & 0.311\end{pmatrix}\begin{pmatrix}R\\G\\B\end{pmatrix}$
	\end{center}
	(A screen manufacturer would change the matrix entries to work for its $RGB$ entries.) Find the equation that converts the $YIQ$ data transmitted by the television
	station to the $RGB$ data needed for the television screen.
}{
  % Solution
	If we consider the equation above to be
	\begin{center}
		$\begin{pmatrix}Y\\I\\Q\end{pmatrix}=A\begin{pmatrix}R\\G\\B\end{pmatrix}$,
	\end{center}
  then
	\begin{center}
		$\begin{pmatrix}R\\G\\B\end{pmatrix}=A^{-1}\begin{pmatrix}Y\\I\\Q\end{pmatrix}=\begin{pmatrix}    1.0031   & 0.9548  &  0.6179 \\
			0.9968  & -0.2707 & -0.6448 \\ 1.0085  & -1.1105  &  1.6996\end{pmatrix}\begin{pmatrix}Y\\I\\Q\end{pmatrix}$
	\end{center}
}
\useproblem{lay:2_7_22}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
